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Home » P'(x) = -\frac5000x^2 - 0.5 - 500apps

P'(x) = -\frac5000x^2 - 0.5 - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 Check using the Pythagorean theorem: \(a^2 + b^2 = c^2\). So, \(7^2 + 24^2 = 49 + 576 = 625 = 25^2\).

📌 It is a right triangle. Use the standard area formula: \(rac{1}{2} imes 7 imes 24 = 84 ext{ cm}^2\).

📌 Solve for \(x\) in the equation \(2x^2 - 8x + 6 = 0\) using the quadratic formula.

📌 The quadratic formula is \(x = rac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).

📌 Compute the discriminant: \((-8)^2 - 4 imes 2 imes 6 = 64 - 48 = 16\).

📌 Then, \(x = rac{8 \pm \sqrt{16}}{4} = rac{8 \pm 4}{4}\).

📌 So, \(x = rac{12}{4} = 3\) or \(x = rac{4}{4} = 1\).

📌 Find the sum of the infinite geometric series with first term 5 and common ratio \(rac{1}{3}\).

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